This invention relates to jig saws or scroll saws which have a saw blade connected between the free ends of the arms of a generally C-shaped or U-shaped member, or yoke, which is reciprocated about a pivot point at the closed end of the yoke to drive the saw blade. The base which supports the reciprocating member is usually provided with a table to support a workpiece, with the saw blade extending through an opening in the table. These saws are designed to reciprocate the saw blade at a high speed. This rapid reciprocation of the yoke creates large inertial forces which can result in severe vibration of the scroll saw. If this vibration is not controlled, the scroll saw will actually move about as a result of the vibration unless it is bolted or otherwise secured to a large mass. In order to overcome this vibration, it has been suggested that a counterbalance be coupled to the motor drive shaft. In this regard, reference is made to the Bill E. Sutton U.S. Pat. No. 4,503,742 dated Mar. 12, 1985, entitled "Precision Saw." The Sutton patent discloses a saw having a C-member which is reciprocated by a motor which rotates a drive shaft which in turn moves an eccentric drive arm coupled with the lower arm of the C-member through a drive linkage. The single counterbalance on the drive shaft has a center of mass offset radially from the axis of the drive shaft in a direction to counter the inertial effects of the reciprocating C-member. With this arrangement, and by selecting a couterbalance of the proper weight, the up and down inertial forces created by the reciprocating yoke or C-member can be effectively cancelled out to thereby reduce vibration. A problem with this type of unit, however, is that although the single counterbalance can be used to effectively eliminate vibration in a vertical direction, the counterbalance itself creates vibration in a horizontal direction. During every rotation of the counterbalance, the offset center of mass will create inertial forces in opposite directions in a horizontal plane. As a result, the saw will move or vibrate back and forth in that horizontal plane, resulting again in an unacceptable amount of movement of the saw.